as well as more room to chase people
There are few times where you should actually be in a chase, it's usually a waste of time or leading you into their team.
On the note of turrets, it depends on the lane. Tops will usually push their turret down then proceed to roam however most mids will push the wave toward the enemy as soon as they hit 6 and move to roam. It occupies the opposing midlaner and forces them to choose between minions doing tower damage and following their opponent or staying and having a 3v2 or 2v1 in a lane not including jungle presence.
Reason for that being your mid is almost always your AP carry, they likely have a better use elsewhere picking up kills or at least assists than sitting in mid and farming endlessly.
Certain mids, mostly mobile assassins with weaker laning phases in comparison to other mids (ex. Katarina, Zed, Talon) will roam at 6 to pick up kills elsewhere more safely than to stay in midlane and become quickly irrelevent.